Tunneling time and Hartman effect in a ferromagnetic graphene superlattice

Abstract

Using transfer-matrix and stationary phase methods, we study the tunneling time (group delay time) in a ferromagnetic monolayer graphene superlattice. The system we peruse consists of a sequence of rectangular barriers and wells, which can be realized by putting a series of electronic gates on the top of ferromagnetic graphene. The magnetization in the two ferromagnetic layers is aligned parallel. We find out that the tunneling time for normal incident is independent of spin state of electron as well as the barrier height and electron Fermi energy while for the oblique incident angles the tunneling time depends on the spin state of electron and has an oscillatory behavior. Also the effect of barrier width on tunneling time is also investigated and shown that, for normal incident, the Hartman effect disappears in a ferromagnetic graphene superlattice but it appears for oblique incident angles when the x component of the electron wave vector in the barrier is imaginary

Observing and interpreting superluminal behaviors in microwave and optical experiments

“…The goodness of the fitting is demonstrated by the adjusted R 2 values of 0.98. In the same graph, we also report the curve relative to a delay for v ≡ c, which is well above that of Equation (8), thus demonstrating the superluminal behavior of the experimental results, up to a distance L ≳ 1 m. A similar result was obtained in the case of near-field outcoming from a superresolving composed pupil, operating with a modulated carrier at 9.33 GHz. 2 By means of a comparison with the curve relative to a delay for v ≡ c, we could there evidence a clear superluminal behavior up to a distance L ' 40 cm.…”

“…Something similar has been obtained in the microwave range by operating with an air gap between two paraffin prisms . Another interesting case is given in Reference .…”

Rashba spin–orbit effect on dwell time in graphene asymmetrical barrier

“…The dwell time was first introduced by Smith, which is defined as the time spent by a particle in the barrier region 0 \ x \ L [21]. Recently, some papers have focused on the group delay and/or dwell time in graphene-based barrier nanostructures [22][23][24][25][26][27][28][29][30]. In this work, we study the dwell time through an asymmetric barrier in monolayer graphene with RSOI, which to the best of our knowledge has not already been reported.…”

Hartman effect from layered PT-symmetric system

“…Many authors have contributed towards this. The earlier experiments have indicated the superluminal nature of the tunneling time [20] and are found to be independent of the thickness of the tunneling region [21,22,23,24,25,26]. The tunneling time was also studied with double barrier optical gratings [25] and double barrier photonic band gaps [27] and is found to be paradoxically short.…”